August 24, 2009

An entire unit of activities for proportional reasoning (including percents). Designed for classes that need to re-teach a lot of middle school content while also meeting high school Algebra I objectives. Also a great resource for middle school teachers. The approach mixes direct instruction with guided inquiry and real-life applications. Students won't get lost, but they will construct some of the concepts themselves and see how the material applies to their lives.

- Mathematics > General
- Mathematics > Algebra

- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Model with mathematics.

Use appropriate tools strategically.

Represent proportional relationships by equations.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

convert units within a measurement system, including the use of proportions and unit rates.

graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and

represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions;

represent linear proportional situations with tables, graphs, and equations in the form of y = kx;

identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and

use data from a random sample to make inferences about a population;

express and interpret relationships symbolically in accordance with accepted theories to make predictions and solve problems mathematically, including problems requiring proportional reasoning and graphical vector addition.

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.